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which opens the door. If the animal is again placed in the cage, it will be able to get out in shorter time on the second trial. In the course of fifteen or twenty trials, he will have learned just what movement to make in order to get out. This is a typical instance of learning by trial and error which can be defined as a varied reaction with gradual elimination of the unsuccessful responses, and the fixation of the successful one. In other words, trial and error learning is learning by doing rather than by reasoning or observation. The animal learns to get out of the cage by getting out, not by seeing how to get out, or reasoning how to get out. Some of the typical examples of trial and error learning in human beings are learning to skate, to write, and to throw a ball.

12. Place of Trial and Error in Learning

[SMITH, Stevenson, and GUTHRIE, Edwin R., General Psychology in Terms of Behavior, pp. 118-119. New York, D. Appleton & Co., 1924.]

Trial and error refers to attempts of an organism to adjust itself to situations by the trial and success method and without foresight of the outcome. First one adjustment is made and then another, until success attends. Trial and error, or trial and success as it has been called, may be a completely random and uncontrolled procedure, or it may be partially under the control of consciousness.

It is believed by some that all learning is by trial and error. Other students of psychology admit of the possibility of learning by ideas or reflection, and by imitation. All agree that the time will never come when trial and error can be entirely eliminated from the learning process. Man's ability to learn through the use of ideas and by reflection furnish us with the key for rapid social progress. It also accounts for the higher forms of intellectual life.

Trial and error enters into the behavior of all animals. When hungry, they are likely to rage about until, after many fruitless reactions, they come at last by chance upon food or the signs of food. In the same way mates are discovered, new shelter is found, or building materials secured. The trial and error behavior of most higher animals differ from that of the lowest

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Most inventions and discoveries are the result of happy accidents. . . . A series of trial and error responses may become a habit in certain cases through the agency of conditioning stimuli in the manner described in the discussion of serial responses. It is very seldom, however, that the series of trial and error responses as a whole becomes fixed as a habit. Usually the series is shortened in the process of habit formation, the final response being given but many of the futile responses that preceded it being eliminated.

13. Factors Involved in Learning by Association [SANDIFORD, Peter, Mental and Physical Life of School Children, pp. 179-181. New York, Longmans, Green & Co., 1913.]

The factors usually given are frequency, recency, vividness, primacy, the resultant satisfaction, the mood of the moment and the relationship between the objects associated. (a) Frequency. The more frequently two objects are associated the easier becomes the process. It is difficult to think of the discovery of America without recalling the name of Columbus; 9 X is associated with 63; and "Humpty dumpty" is invariably associated with "Sat on a wall." Repetition or frequency is the chief cause of the association. These things have occurred so often together in our experience that it is only with the utmost difficulty that we can now dissociate them. Drill or practice in school-work receives its sanction from this principle. (b) Recency. The traces left behind in our nervous system by events of to-day are deeper than those of a year ago. It is fairly easy to recall the drift of yesterday's sermon in church but the sermon of a month ago seems entirely to have disappeared. And so with other things. Teachers have recapitulatory lessons because children forget the past so easily. They invoke the power both of frequency and recency to aid them in making clear association in the minds of their pupils. (c) Vividness. Some sermons because of the vividness of their presentation, make a deeper impression than others. Hence vividness is an important factor in association. "I shall never forget it until my dying day" refers to some particularly vivid association. The reason children learn more quickly from one teacher than another is partly by reason of the vividness of presentation. But we must remember that vividness is a relative term. In

order that mountains may appear high we must have then the trast of deep valleys. (d) Primacy. "First impressions ond strongest." . . . First impressions of the theater are often m influential partly because of the vividness of the occasion, bu also because of their primacy. If on our first introduction to a volcano the idea of a burning mountain is associated with it, the connection persists in a most troublesome manner; sometimes years of teaching fail to dispel the incorrect information. . . (e) The resultant satisfaction. The normal human mind loves to dwell on the pleasant things in life and shuns the contemplation of the unpleasant. . . . Those situations which resulted in satisfaction at the time of their occurrence stand a much better chance of becoming associated than others. The importance of this great law is not sufficiently emphasized in school-room practice. And it is often forgotten that the satisfaction which comes from completing a hard task is one of the great and pure satisfactions of this life. (f) The Mood of the Moment. If we are in a despondent mood our whole outlook is tinged with despondency. Dismal associations are aroused by stimuli, which, on other days, would have aroused nothing but pleasant thoughts. These moods are valuable signs of bodily health. . . . (g) The relationship existing between the objects. In the parlor game, where a tray containing thirty or forty different objects is shown to us for a short time and we are told to name as many as we can remember, we try to make artificial associations. It is, however, a difficult task. Where the relationship between objects is slight or non-existent, associations are only formed after great exertion; where natural relationships exist associations are easily formed. . . . The various number rhymes and number games are excellent examples of this principle of relationship..

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14. Thorndike's Combination Law of Association [THORNDIKE, E. L., Elements of Psychology, p. 249. New York, A. G. Seiler, 1905.]

Any fact thought of will call up that fact, the thought of which has accompanied or followed it or a part of it most frequently, most recently, in the most vivid experience and with the most resultant satisfaction, and which is most closely connected with the general set of the mind at the time.

15. Curves of Learning

[STARCH, Daniel, Educational Psychology, pp. 141-143. Copyright, 1920, by the Macmillan Co.] (Adapted.)

The Curve of Learning.-The rate and progress of learning may be expressed in terms of the amount done per unit

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Sending

Slowest Main Line Rate

Receiving

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of work. The relation between these two variables is represented by the curve of learning in which one function, usually time, is represented along the base line, and

12 16 20 24 28 32 30 the other, usually amount

Weeks of Practice

FIG. 12. DIAGRAM SHOWING IM-
PROVEMENT IN SENDING AND RE-
CEIVING TELEGRAPHIC MESSAGES.

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accomplished, is represented along the vertical axis. Figure 12 represents a typical curve of learning in which progress is measured by the amount achieved per week of practice. It shows the improvement made in sending and receiving messages.

Certain characteristics of learning curves may be noted in the figures shown. Most of the learning curves we have are based upon studies made typewriting, mirror tracing,

FIG. 13. IMPROVEMENT IN LEARNING
TELEGRAPHY ANALYZED GRAPHI-
CALLY. INDIVIDUAL, J. S.
(After Bryan and Harter.}

in the learning of such skills as
ball tossing, learning substitutions, and the like. Almost
nothing has been done to study the progress of learning the
school subjects, or the acquisition of ideals and attitudes.
Consequently most of our generalizations are based upon
the former kind of learning. An inspection of the learn-
ing curves given herewith shows an initial period of rapid
progress, and successive periods of little or no progress which
are followed by periods of rapid progress. It is not claimed

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5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Days

FIG. 14. CURVE SHOWING PROGRESS MADE IN LEARNING RUSSIAN. (From The Mind in the Making, by Edgar James Swift. Copyright, 1908. Courtesy of Charles Scribner's Sons.)

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Amount of Practice in Hours

FIG. 15. LEARNING CURVES SHOWING IMPROVEMENT MADE IN TYPE

WRITING BY THE SIGHT METHOD.

(After Book. Courtesy of the Gregg Publishing Company.)

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